Turns out,
MPQ master v1.2.0 is the better tool. But the procedure is still pretty much the same. Open MPQ Master, go to File -> Open, find the related MPQ file ( As explained by
@Ravager16829 )
In your case, the related MPQ files are
not War3.mpq and War3x.mpq, but
War3xlocal.mpq and
War3Patch.mpq, make sure to select Warcraft III when you are prompted to select a listfile. When you're done just browse through the folder and find the campaign files you want to extract, right click on said file and then extract it somewhere on your computer.